English

Permutation Complexity of the Thue-Morse Word

Combinatorics 2010-04-06 v2

Abstract

Given a countable set X (usually taken to be the natural numbers or the integers), an infinite permutation \pi of X is a linear ordering of X. This paper investigates the combinatorial complexity of the infinite permutation on the natural numbers associated with the well-known and well-studied Thue-Morse word. A formula for the complexity is established by studying patterns in subpermutations and the action of the Thue-Morse morphism on the subpermutations.

Keywords

Cite

@article{arxiv.1003.6123,
  title  = {Permutation Complexity of the Thue-Morse Word},
  author = {Steven Widmer},
  journal= {arXiv preprint arXiv:1003.6123},
  year   = {2010}
}
R2 v1 2026-06-21T15:05:11.310Z